SR paradox - help!
DavidBowman
prove his aether theory. He got the tongue-lashing he deserved... but
the problem still haunts me.
So I want to expand and instantiate it, and present it as a legitimate
paradox that I can't resolve -- but hopefully you can, if you would be
so very kind.
======
The Bureau of Standards sets up two identical beacons. The one on
earth fires an omnidirectional radio pulse. When that energy reaches
the moon one second later, it's twin beacon on the moon detects it and
fires another omnidirectional burst.
One second after that, the radio pulse from the moon reaches earth and
is detected by the earth beacon which fires another omnidirectional
blast ...and so on.
Each beacon is triggered by the other, and alternately fires a radio
pulse every two seconds. So a guy on Mars hears a "click" on his radio
reciever at one-second intervals.
So far, so good.
BUT:
A guy in a spaceship moving .999c must also hear the same clicks at
one-second intervals, since we all agree that the earth-moon distance
is one light-second, and c is the same for everybody.
The problem is that this gizmo can be used as a universal time standard
-- literally. Everyone in the universe can listen to the master clock
ticking away once per second, no matter how fast they're moving --
including the two guys in the twin paradox.
The only way out I can see is if time dialation causes the guy in the
spaceship to observe a light pulse travel from the earth to the moon in
an arbitrarily short time, limited only by how fast his rocket can go.
But if that's the case, you can get superluminal communication,
because:
1) you can make radio travel from the earth to the moon in an
arbitrarily short time, and
2) the space ship is a finite number of earth-moon distances away.
=========
"Well Hal, I'm damned if I can find anything wrong with it!"
-- David Bowman to HAL9000 in the pod bay
=[ d
dlzc1 D:cox T:net@nospam.com N:dlzc D:aol T:com (dlzc)
"DavidBowman" <dt04...@yahoo.com> wrote in message
news:1107656113....@c13g2000cwb.googlegroups.com...
> This question was inspired by a single sentence in a post by Kenseto to
> prove his aether theory. He got the tongue-lashing he deserved... but
> the problem still haunts me.
>
> So I want to expand and instantiate it, and present it as a legitimate
> paradox that I can't resolve -- but hopefully you can, if you would be
> so very kind.
>
> ======
>
> The Bureau of Standards sets up two identical beacons. The one on
> earth fires an omnidirectional radio pulse. When that energy reaches
> the moon one second later, it's twin beacon on the moon detects it and
> fires another omnidirectional burst.
>
> One second after that, the radio pulse from the moon reaches earth and
> is detected by the earth beacon which fires another omnidirectional
> blast ...and so on.
>
> Each beacon is triggered by the other, and alternately fires a radio
> pulse every two seconds. So a guy on Mars hears a "click" on his radio
> reciever at one-second intervals.
On Mars, it will only be at one second intervals when the Moon is located
transverse to the line-of-sight between the Mars and Earth. When the Moon
is closest to Mars, he'll get a double pulse each two seconds. When the
Moon is opposite Mars, he'll also get a double pulse each two seconds!
> So far, so good.
>
> BUT:
> A guy in a spaceship moving .999c must also hear the same clicks at
> one-second intervals, since we all agree that the earth-moon distance
> is one light-second, and c is the same for everybody.
No. Same type of co-location problem, PLUS time dilation. You didn't
specify if the "guy" was travelling towards, away from, or parallel to the
Earth-Moon system.
> The problem is that this gizmo can be used as a universal time standard
> -- literally. Everyone in the universe can listen to the master clock
> ticking away once per second, no matter how fast they're moving --
> including the two guys in the twin paradox.
Sorry, no. And depending on the motion, the Moon is not *observed* to be
"one light second" from the Earth.
> The only way out I can see is if time dialation causes the guy in the
> spaceship to observe a light pulse travel from the earth to the moon in
> an arbitrarily short time, limited only by how fast his rocket can go.
>
> But if that's the case, you can get superluminal communication,
> because:
>
> 1) you can make radio travel from the earth to the moon in an
> arbitrarily short time, and
>
> 2) the space ship is a finite number of earth-moon distances away.
Time dilation is no respector of what you "arbitrarily assume" about a
pulse source. Even a pair of them.
David A. Smith
DavidBowman
located
transverse to the line-of-sight between the Mars and Earth.
Oww!
yes, of course!
So have the moon beacon signal beamed directionally to earth. Anyone
in space will now see a clock tick every two seconds instead, the
round-trip time of light which is supposedly invariant from everyone's
point of view.
The basic problem is light appearing to move at the same speed for
people experiening different rates of time passing, and I don't see
that going away.
Okay, say someone at .999c moves away from the solar system
perpendicular to the ecliptic plane. He looks back and sees
everything speeded up.
The planets whizz around the sun, ships appear to fly from earth to
the moon in minutes, the seasons are observed to pass in days, and a
flash of light on earth reflects off of the moon in what appears to be
a millisecond.
Doesn't that mean that light appears to move faster than c, and that,
given another contrived scenario, can be used for superluminal
communication.
Obviously it can't. I just want to know why.
=[ d
dlzc1 D:cox T:net@nospam.com N:dlzc D:aol T:com (dlzc)
"DavidBowman" <dt04...@yahoo.com> wrote in message
news:1107663546.1...@o13g2000cwo.googlegroups.com...
>> On Mars, it will only be at one second intervals when the
>> Moon is located transverse to the line-of-sight between the
>> Mars and Earth.
>
> Oww!
> yes, of course!
>
> So have the moon beacon signal beamed directionally to
> earth. Anyone in space will now see a clock tick every
> two seconds instead, the round-trip time of light which is
> supposedly invariant from everyone's point of view.
Only for those that are at rest wrt the Earth. Time dilation is an
observable. If affects heartbeats, "2-second" clock pulses, and the
frequency of observed light.
> The basic problem is light appearing to move at the same speed for
> people experiening different rates of time passing, and I don't see
> that going away.
It actually isn't a problem, since it is one of the laws of physics that is
expected not to vary.
> Okay, say someone at .999c moves away from the solar system
> perpendicular to the ecliptic plane. He looks back and sees
> everything speeded up.
If he/she factors out the Doppler shift, yes.
> The planets whizz around the sun, ships appear to fly from earth to
> the moon in minutes, the seasons are observed to pass in days, and a
> flash of light on earth reflects off of the moon in what appears to be
> a millisecond.
OK. But keep in mind the observed rotation of the geometry of the ecliptic
plane. The ecliptic (and the Moon) will not appear to perpendicular to the
line of flight...
> Doesn't that mean that light appears to move faster than c, and that,
> given another contrived scenario, can be used for superluminal
> communication.
>
> Obviously it can't. I just want to know why.
Because it is simply a matter of perspective. An illusion. It happens in
a different "slice" of spacetime than yours.
David A. Smith
The TimeLord
I meant it to go to the NG, but before I realized what was happening, my OS
had already done the dirty deed. (Obviously my return address is munged,
because I've had too many offers from some people to go chase their
favorite UFO.)
DavidBowman <dt04...@yahoo.com> wrote on Saturday 05 February 2005 20:15 in
<1107656113....@c13g2000cwb.googlegroups.com> posted to
sci.physics.relativity:
> This question was inspired by a single sentence in a post by Kenseto to
> prove his aether theory. He got the tongue-lashing he deserved... but
> the problem still haunts me.
Sorry I missed the original thread; it must have been interesting.
[...]
> The Bureau of Standards sets up two identical beacons. The one on
> earth fires an omnidirectional radio pulse. When that energy reaches
> the moon one second later, it's twin beacon on the moon detects it and
> fires another omnidirectional burst.
>
> One second after that, the radio pulse from the moon reaches earth and
> is detected by the earth beacon which fires another omnidirectional
> blast ...and so on.
>
> Each beacon is triggered by the other, and alternately fires a radio
> pulse every two seconds. So a guy on Mars hears a "click" on his radio
> reciever at one-second intervals.
>
> So far, so good.
>
> BUT:
> A guy in a spaceship moving .999c must also hear the same clicks at
> one-second intervals, since we all agree that the earth-moon distance
> is one light-second, and c is the same for everybody.
Yes, c is the same for everybody. However, the underlying "essence" of SR is
that things that are simultaneous in one frame are not necessarily
simultaneous in another. If you work through the twin-paradox problem, the
solution is actually that for the Earth-bound twin, the clock on the
spacecraft has run slow, but for the spacecraft-bound twin, it's the trip
that has been shrunk. That fact can be easily shown from the Lorentz
transformation.
>
> The problem is that this gizmo can be used as a universal time standard
> -- literally. Everyone in the universe can listen to the master clock
Mmmmmm. Gotta be careful with that one. At face value, what you say is
correct, but knowing some of the types on the internet, it will be promptly
taken out of context, misapplied and then used and abused to "prove" SR
wrong.
> ticking away once per second, no matter how fast they're moving --
> including the two guys in the twin paradox.
However, the "ticking away once per second" is a type of frequency that is
measured in the rest frame of the Earth-Moon system. For the guy going
99.9%c, the period of the ticks will undergo time dilation.
>
> The only way out I can see is if time dialation causes the guy in the
> spaceship to observe a light pulse travel from the earth to the moon in
> an arbitrarily short time, limited only by how fast his rocket can go.
If f0 = 1 Hz = frequency in Earth-Moon system (rest)
= 1/T0
and f = frequency of guy going 99.9%c
= 1/T
then T = 1/f = T0 * Sqrt[1 - 0.999^2]
= 1/f0 * Sqrt[1.999e-3]
then f = f0 * 1/0.0447
= 22.37 * f0
So the guy at 99.9%c sees 22.37 ticks per second, regardless of the
directions of his travel due to time dilation. This is different from the
Doppler shift in the carrier frequency, would be blue shifted if he is
going toward Earth and red-shifted if traveling away. The distinction
between the two is due to the way time dilation results and the definitions
work in one case and the fact that Doppler shift depends on the wave nature
of light in the other case.
>
> But if that's the case, you can get superluminal communication,
> because:
>
> 1) you can make radio travel from the earth to the moon in an
> arbitrarily short time, and
[smile] No that does not follow. The signals still travel at speed c. Due to
the velocity-addition formula, they are still limited by c.
>
> 2) the space ship is a finite number of earth-moon distances away.
[big smile] Zeno's paradox eh? As I recall, Achilles won the race anyway and
didn't loose until he went to Troy. - Seriously, FTL signaling still
doesn't follow from that.
--
// The TimeLord says:
// Pogo 2.0 = We have met the aliens and they are us!
The TimeLord
Saturday 05 February 2005 20:58 in <6JfNd.17543$Yu.7848@fed1read01> posted
to sci.physics.relativity:
> Dear DavidBowman:
>
> "DavidBowman" <dt04...@yahoo.com> wrote in message
> news:1107656113....@c13g2000cwb.googlegroups.com...
[...]
> On Mars, it will only be at one second intervals when the Moon is located
> transverse to the line-of-sight between the Mars and Earth. When the Moon
> is closest to Mars, he'll get a double pulse each two seconds. When the
> Moon is opposite Mars, he'll also get a double pulse each two seconds!
How do you figure this? The relativistic effects only take over when there
is relative motion or there is space-time curvature. How does
"transverse...line-of-sight" have anything to do with it?
>
>> So far, so good.
>>
>> BUT:
>> A guy in a spaceship moving .999c must also hear the same clicks at
>> one-second intervals, since we all agree that the earth-moon distance
>> is one light-second, and c is the same for everybody.
>
> No. Same type of co-location problem, PLUS time dilation. You didn't
> specify if the "guy" was travelling towards, away from, or parallel to the
> Earth-Moon system.
I think he was asking about relativistic effects. The Doppler effect comes
about from the wave nature of light and thus would pertain to the carrier
and not the info on the carrier.
>
>> The problem is that this gizmo can be used as a universal time standard
>> -- literally. Everyone in the universe can listen to the master clock
>> ticking away once per second, no matter how fast they're moving --
>> including the two guys in the twin paradox.
>
> Sorry, no. And depending on the motion, the Moon is not *observed* to be
> "one light second" from the Earth.
The Moon's orbit is roughly circular, so it is not moving radially with
respect to the Earth. So by the derivation of the Lorentz transformation,
it's motion isn't significant. Anyway, the moon isn't going that fast
anyway, so the relativistic effects are approximately insignificant.
[...]
> Time dilation is no respector of what you "arbitrarily assume" about a
> pulse source. Even a pair of them.
That still doesn't get to the heart of what he is asking, which I think is a
pretty good point, even though Relativity does provide an answer.
The TimeLord
<1107672540....@l41g2000cwc.googlegroups.com> posted to
sci.physics.relativity:
>> Because it is simply a matter of perspective. An illusion.
>
> I know! And I believe that! But I have this compulsive...compulsion
Please don't. [smile] David Smith seems to be introducing unnecessary
obfuscation that really doesn't have anything to do with your question.
> to leap on apparant contradictions and resolve them.
>
> In SR, the only way to think about them is in wierd-ass gedankin
> experiments. That's why Einstein did it. If you get sick of it, I
Actually there are plenty of actual experiments that have tested SR and to
some extent GR. All have been substantiated Einstein within the limits of
the equipment used in the experiments.
[...]
> A spaceship starts from earth and moves away from earth at near c.
>
> The pilot looks out the back window and sees flights between the earth
> and the moon apparantly taking minutes, and communication from earth to
> Pluto (2 billion miles) taking 5 seconds. It appears to be
> superluminal communication, but it's only an illusion due to Lorentz
> and his gamma. The people on earh and pluto think it takes hours.
Does he _really_ think it takes 5 seconds? I don't think so. Anyway, the
gamma in the Lorentz transformation is due to a real effect and not to any
illusion. The real effect is that time is different in different frames of
reference unless they are at rest with each other. In fact
gamma = dt/dT
where t = observed time (any frame)
T = proper time (in frame that is at rest with object under
observation)
As a consequence of this, distances can't be absolute things either,
especially if there are absolute laws like conservation of energy and
conservation of momentum.
As a result of that, things that are simultaneous, such a measuring the two
ends of a distance are not simultaneous in a different frame. So how do you
know how far a distance is when you can't see the two ends simultaneously?
The Lorentz transformation tells you:
x' = gamma (x - v t)
Bottom line of the Lorentz transformation L:R^4->R^4 is the following. The
events (points in R^4) are always fixed, but how we view the events depends
on our frame of reference. Once people understand that, Relativity becomes
pretty simple.
At any rate, the guy moving at 99%c would see his trip shorter; 14% of what
Earthlings see. However Earthlings see the guy at 99%c as aging only 14% of
what is happening on Earth. When Earthlings calculate his speed, it is
v=l/t. When he calculates his speed, it's v=l'/t'=14%l/14%t=l/t. The both
agree on the speed, but that's about it.
>
> But it so happens that the spaceship is also 2 billion miles away from
> earth. It went that far, decellerated, and now just sits there in
> space.
>
> Surely, being the same distance, radio from earth to the spaceship
> would also take the same 5 seconds, as measured by the spaceship.
No. We actually have something that approximates what you are now
describing: Neptune, about 20 AU away. In fact Voyager 2, which was at
Neptune taking some pictures had a communications link with the Deep Space
Network on Earth. Both Earth and Voyager 2 agreed that a command sent from
Earth to the probe took about 2.8 hours to arrive and the acknowledgment
took about 2.8 hours to get to Earth. Of course Voyager was not moving at
relativistic speeds.
[...]
> BUT:
> Suppose a twin spacecraft left earth at the same time, going the
> opposite direction. His clock runs at the same rate as the other space
> ship's, and if they returned to earth, both pilots' wristwatches would
> show the same time.
Yes.
>
> Each pilot (at rest relative to earth), sees radio waves apparantly
> cross the two billion miles from earth to pluto (or to his spacecraft)
> in five seconds.
Well, not 5 second, but I get your idea and it's ok.
>
> Now, the ships are frour billion miles apart, so Earth is used as a
> repeater, rebroadcasting the weak signal recieved from each space ship
> at higher power (omnidirectionally)
Ah, but they are in different reference frames. In fact, when the are moving
apart at speed v from Earth, then they are moving at speed
u = 2*v / (1 + v^2/c^2)
from each other. This is the result of the velocity-addition formula.
There is an actual instant of this sort of thing: M-87 in Ursa Major. One of
the gas-jets from the galaxy is shot out toward Earth at about 99%c. The
other gas-jet is moving away from Earth at about 75%c. (I might not have
the numbers exactly right; it's been a while.) At any rate, they are moving
away from each other at
(75%c+99%c) / (1 + (75%)(99%))
= 174%c / (1 + 74.25%)
= 99.86%c (not 174%c)
[...]
> Note that trhe answer isn't "because SR says so" or "the whole thing is
> an illusion". I KNOW that SR says so, and I KNOW that it's an
> illusion!
I _do_ like your attitude. However, the effect is not an illusion as the
meson experiment by David H Frisch and James H Smith has shown.
[...]
DavidBowman
I know! And I believe that! But I have this compulsive...compulsion
to leap on apparant contradictions
and resolve them.
In SR, the only way to think about them is in
wierd-ass gedankin experiments.
That's why Einstein did it.
If you get sick of it, I understand.
You don't have to be as singleminded about contradictions (paradoxes)
as as I am!
But having said that...
=======
A spaceship starts from earth and moves
away from earth at near c.
The pilot looks out the back window and
sees flights between the earth
and the moon apparantly taking minutes, and
communication from earth to
Pluto (2 billion miles) taking 5 seconds.
It appears to be superluminal communication,
but that's only an illusion due to Lorentz
and his gamma. To the people on earh and pluto,
communication takes hours.
But it so happens that the spaceship is also
2 billion miles away from earth. And surely,
being the same distance asd Pluto, radio from
earth to the spaceship would also take the same
5 seconds, as measured by the spaceship.
Of course it's also illusory; two-way
conversations about what's
happening on earth refer to events
which happen many hours apart (on
earth).
BUT:
Suppose a twin spacecraft left earth
at the same time, going the opposite
direction. His clock runs at the same
rate as the other space ship's, and if
they returned to earth, both pilots'
wristwatches would show the same time.
Each pilot sees radio waves apparantly
cross the two billion miles from earth
to pluto (and to his spacecraft) in five seconds.
Since the ships are four billion miles
apart, Earth is used as a repeater,
rebroadcasting the weak signal recieved
from either space ship at higher power (omnidirectionally)
Ten seconds after saying "hello", pilot A
hears himself echoed from earth as it is rebroadcast.
He can assume that pilot B heard it too at
the same time, as the EM wave crossed the
same distance to both ships.
Pilot B says "hello" back, and in a
symmetric situation, sees the wave
take 10 seconds to get back to A,
even though earth swears there were
several hours between the two messges.
SO:
The pilots see their message propagate 4 billion
miles in 10 seconds (i.e., superluminaly).
Why can't they chat by radio with an apparant round-trip delay of only
20 seconds?
You see the contradiction?
What's the resolution?
Note that trhe answer isn't "because SR
says so" or "the whole thing is an illusion".
I KNOW that SR says so, and I KNOW that
it's an illusion!
If you find the whole thing silly or boring,
that's perfectly okay; I completely understand!
But to ME, I want to resolve the contradiction.
I just want to know what part of the scenario wouldn't happen, and why.
=[ d
TomGee
N:dlzc D:aol T:com (dlzc) wrote:
> Dear DavidBowman:
>
> "DavidBowman" <dt04...@yahoo.com> wrote in message
> news:1107663546.1...@o13g2000cwo.googlegroups.com...
> >> On Mars, it will only be at one second intervals when the
> >> Moon is located transverse to the line-of-sight between the
> >> Mars and Earth.
> >
> >
>
>
> > Okay, say someone at .999c moves away from the solar system
> > perpendicular to the ecliptic plane. He looks back and sees
> > everything speeded up.
>
> If he/she factors out the Doppler shift, yes.
>
>
think what you two think because it is counter-intuitive to say
otherwise. I don't remember offhand where I learned that, but Bowman,
this is another one of those contradictions to common sense which you
feel you must resolve, so maybe you can find out who's right, you and
Smith, or me.
TomGee
dlzc1 D:cox T:net@nospam.com N:dlzc D:aol T:com (dlzc)
"The TimeLord" <mathnphy...@hotmail.com> wrote in message
news:110bk56...@corp.supernews.com...
> N:dlzc D:aol T:com (dlzc) <N: dlzc1 D:cox T:n...@nospam.com> wrote on
> Saturday 05 February 2005 20:58 in <6JfNd.17543$Yu.7848@fed1read01>
> posted
> to sci.physics.relativity:
>
>> Dear DavidBowman:
>>
>> "DavidBowman" <dt04...@yahoo.com> wrote in message
>> news:1107656113....@c13g2000cwb.googlegroups.com...
> [...]
>> On Mars, it will only be at one second intervals when the Moon is
>> located
>> transverse to the line-of-sight between the Mars and Earth. When the
>> Moon
>> is closest to Mars, he'll get a double pulse each two seconds. When the
>> Moon is opposite Mars, he'll also get a double pulse each two seconds!
>
> How do you figure this? The relativistic effects only take over when
> there
> is relative motion or there is space-time curvature. How does
> "transverse...line-of-sight" have anything to do with it?
You be on Mars, with excellent eyesight.
When the Moon is transverse to the line of sight between Earth and Mars,
then the two signals (originally discussed) are fully separated, and
barring significant relative velocity, you'd see each pulse from Earth
arrive one second after each pulse from the Moon (or vice versa).
When the Moon is closest to you, you get the outbound pulse from Earth *in
sync* with the outbound pulse from the Moon. The Moon's pulse is emitted
as Earth's "passes" it.
And when the Moon is farthest from you, the Earth's outbound pulse is sent
at the same time as the Moon's arrival.
It is just geometry...
>>> So far, so good.
>>>
>>> BUT:
>>> A guy in a spaceship moving .999c must also hear the same clicks at
>>> one-second intervals, since we all agree that the earth-moon distance
>>> is one light-second, and c is the same for everybody.
>>
>> No. Same type of co-location problem, PLUS time dilation. You didn't
>> specify if the "guy" was travelling towards, away from, or parallel to
>> the
>> Earth-Moon system.
>
> I think he was asking about relativistic effects. The Doppler effect
> comes
> about from the wave nature of light and thus would pertain to the carrier
> and not the info on the carrier.
He was asking about relativistic effects, AND he invoked a trivial side
issue which I discussed.
>>> The problem is that this gizmo can be used as a universal time standard
>>> -- literally. Everyone in the universe can listen to the master clock
>>> ticking away once per second, no matter how fast they're moving --
>>> including the two guys in the twin paradox.
>>
>> Sorry, no. And depending on the motion, the Moon is not *observed* to
>> be
>> "one light second" from the Earth.
>
> The Moon's orbit is roughly circular, so it is not moving radially with
> respect to the Earth. So by the derivation of the Lorentz transformation,
> it's motion isn't significant. Anyway, the moon isn't going that fast
> anyway, so the relativistic effects are approximately insignificant.
Yet when the Moon is in line of sight of the moving observer
(Earth-Moon-observer co-linear, a condition he disallowed on his answering
post), length contraction turns the "circular" orbit into a *very*
elliptical orbit.
> [...]
>> Time dilation is no respector of what you "arbitrarily assume" about a
>> pulse source. Even a pair of them.
>
> That still doesn't get to the heart of what he is asking, which I think
> is a
> pretty good point, even though Relativity does provide an answer.
To get at the goodies inside a fruit, sometimes you cut away at rind. He
finally settled on a two second pulse from Earth, which should be much
closer to all his paradox requires.
David A. Smith
dlzc1 D:cox T:net@nospam.com N:dlzc D:aol T:com (dlzc)
"DavidBowman" <dt04...@yahoo.com> wrote in message
news:1107683489.6...@g14g2000cwa.googlegroups.com...
>> Because it is simply a matter of perspective. An illusion.
>
> I know! And I believe that! But I have this compulsive...compulsion
> to leap on apparant contradictions
> and resolve them.
>
> In SR, the only way to think about them is in
> wierd-ass gedankin experiments.
> That's why Einstein did it.
>
> If you get sick of it, I understand.
> You don't have to be as singleminded about contradictions (paradoxes)
> as as I am!
I am not faulting you. I am but pointing out complexities that are not
required.
> But having said that...
>
> =======
>
> A spaceship starts from earth and moves
> away from earth at near c.
>
> The pilot looks out the back window and
> sees flights between the earth
> and the moon apparantly taking minutes, and
> communication from earth to
> Pluto (2 billion miles) taking 5 seconds.
> It appears to be superluminal communication,
> but that's only an illusion due to Lorentz
> and his gamma. To the people on earh and pluto,
> communication takes hours.
And if it is light that is carrying communication, how can it be
superlumenal? Keep in mind that c is a local speed "limit". Shapiro time
delay shows that c is a function of path through curved space (just as an
example, not obfuscation).
> But it so happens that the spaceship is also
> 2 billion miles away from earth. And surely,
> being the same distance as Pluto, radio from
> earth to the spaceship would also take the same
> 5 seconds, as measured by the spaceship.
Better, round trip would be 10+ seconds ship-time
> Of course it's also illusory; two-way
> conversations about what's
> happening on earth refer to events
> which happen many hours apart (on
> earth).
>
> BUT:
> Suppose a twin spacecraft left earth
> at the same time, going the opposite
> direction. His clock runs at the same
> rate as the other space ship's, and if
> they returned to earth, both pilots'
> wristwatches would show the same time.
>
> Each pilot sees radio waves apparantly
> cross the two billion miles from earth
> to pluto (and to his spacecraft) in five seconds.
>
> Since the ships are four billion miles
> apart, Earth is used as a repeater,
> rebroadcasting the weak signal recieved
> from either space ship at higher power (omnidirectionally)
>
> Ten seconds after saying "hello", pilot A
> hears himself echoed from earth as it is rebroadcast.
> He can assume that pilot B heard it too at
> the same time, as the EM wave crossed the
> same distance to both ships.
NOT 10 seconds. Your chosen gamma puts the ships much further out than
this, so if one does something in 5 seconds, it'll be close to 15 seconds
before ship A hears his echo. If B started out at the same time, it'll be
~15 seconds for him also. And the distance between the ships and Earth is
contracted, and appears to be consistent with c/t. Only knowing the
distance to Pluto, *as measured in another frame*, raises the
contradiction. Frame jumps do this.
> Pilot B says "hello" back, and in a
> symmetric situation, sees the wave
> take 10 seconds to get back to A,
> even though earth swears there were
> several hours between the two messges.
>
> SO:
> The pilots see their message propagate 4 billion
> miles in 10 seconds (i.e., superluminaly).
> Why can't they chat by radio with an apparant round-trip delay of only
> 20 seconds?
>
> You see the contradiction?
> What's the resolution?
Don't frame jump. At the heart of all this is frame jumping.
> Note that trhe answer isn't "because SR
> says so" or "the whole thing is an illusion".
> I KNOW that SR says so, and I KNOW that
> it's an illusion!
>
> If you find the whole thing silly or boring,
> that's perfectly okay; I completely understand!
>
> But to ME, I want to resolve the contradiction.
> I just want to know what part of the scenario wouldn't happen, and why.
Your conundrum of observing transverse communications (Earth-Moon) will be
much more fruitful. You should stick with that. It is still communication
at c, but appears to be gamma*c.
David A. Smith
Martin Hogbin
"DavidBowman" <dt04...@yahoo.com> wrote in message news:1107656113....@c13g2000cwb.googlegroups.com...
> This question was inspired by a single sentence in a post by Kenseto to
> prove his aether theory. He got the tongue-lashing he deserved... but
> the problem still haunts me.
>
> So I want to expand and instantiate it, and present it as a legitimate
> paradox that I can't resolve -- but hopefully you can, if you would be
> so very kind.
>
> ======
>
> The Bureau of Standards sets up two identical beacons. The one on
> earth fires an omnidirectional radio pulse. When that energy reaches
> the moon one second later, it's twin beacon on the moon detects it and
> fires another omnidirectional burst.
>
> One second after that, the radio pulse from the moon reaches earth and
> is detected by the earth beacon which fires another omnidirectional
> blast ...and so on.
>
> Each beacon is triggered by the other, and alternately fires a radio
> pulse every two seconds. So a guy on Mars hears a "click" on his radio
> reciever at one-second intervals.
>
> So far, so good.
Using the moon is an unnecessary complication since it
orbits the earth. Why not have two beacons a fixed distance
of one light second apart. In fact, for most of what you ask,
you could just have one beacon sending out pulses once
per second.
BUT:
> A guy in a spaceship moving .999c must also hear the same clicks at
> one-second intervals, since we all agree that the earth-moon distance
> is one light-second, and c is the same for everybody.
No, the guy in the spaceship will certainly not receive
the pulses at one second intervals and will not measure
them to be at one second intervals either.
Martin Hogbin
DavidBowman
the ships much further out than this, so if one does
something in 5 seconds, it'll be close to 15 seconds
Aggghhh!
I'm trying to keep away from quantifying all this.
I probably have the wrong distance to pluto, too!
It doesn't matter if the echo is 10 or 15 seconds
at 2 billion miles. If it's less than several hours, it's
superluminal.
> And the distance between the ships and Earth is
> contracted
No it isn't! The length of the ship, as observed from earth, is
contracted.
> Don't frame jump. At the heart of all this is frame jumping.
Yes, thank you! Frame jumping!
The point I'm trying (without much success) is that, while each
inertial frame is
it's own separate "world" with it's own clocks,
and you can't jump between them
without accelerating.
But Light is a little imp that causes a paradox
that I can't resolve. It DOES jump betwen frames
without accellerating, and by using it as
a vector for interactions, the people in
disparate reference frames can interact
without enterring the others' frame.
> And if it is light that is carrying communication, how can it be
superlumenal?
Thank you again! That's the contradiction I'm trying to resolve!
> Keep in mind that c is a local speed "limit".
Right. But when the astronaut looks back, he sees ships flying to the
moon in minutes and messages being sent to mars in seconds.
The latter appears to the astronaut to be superluminal.
He would also observe uranium on earth decaying at a slower rate than
is physically possible.
The contradiction arises because you can use
light to communicate without accellerating,
you can interact with another frame WITHOUT
jumping into it.
My concern isn't that the astronaut sees
appparantly-impossible things. That's just an
interesting consequence of peeing into another
inertial refrence frame.
=[ d
DavidBowman
PEEKING into another inertial refrence frame.
Jeezus, wot next...
=[ d
Tom Capizzi
Why should the guy in the spaceship hear clicks at one-second intervals?
There is a relativistic Doppler shift between him and the source.
Can this be correct? According to relativity, it is the clock which slows
down, along with all physical processes that occur. Shouldn't the time
between ticks appear to be stretched, and the observed frequency be
lower? If we extrapolate this line of reasoning to a relative velocity of
c, then when clocks freeze, frequency would seem to be infinite. It takes
22.37 seconds of the traveler's clock before 1 second elapses of the
earth-moon clock. This is the same prediction that an earth observer
would make about the traveler's clock. To get a frequency of 22.37 * fo
implies counting ticks in one frame and measuring time in the other.
dlzc1 D:cox T:net@nospam.com N:dlzc D:aol T:com (dlzc)
"DavidBowman" <dt04...@yahoo.com> wrote in message
news:1107716776.0...@l41g2000cwc.googlegroups.com...
>> NOT 10 seconds. Your chosen gamma puts
>> the ships much further out than this, so if one does
>> something in 5 seconds, it'll be close to 15 seconds
>
> Aggghhh!
> I'm trying to keep away from quantifying all this.
> I probably have the wrong distance to pluto, too!
A slight change in gamma can fix this. Details are not important yet.
> It doesn't matter if the echo is 10 or 15 seconds
> at 2 billion miles. If it's less than several hours, it's
> superluminal.
That is the point. The distance between the ship and the Earth is
*contracted*, from the ship's point of view. Length contraction is
symmetric. It may not have the same value for each frame, but it is always
contracted.
>> And the distance between the ships and Earth is
>> contracted
>
> no it isn't! The length of the ship, as observed from earth, is
> contracted.
Yes. Think again. No special frames, the effects are always observed.
Only Earth distances (which are nearly at rest) arrive at "2 billion
miles". Ship distance is *always* the same or less.
>> Don't frame jump. At the heart of all this is frame jumping.
>
> Yes, thank you! The point I'm trying (without much success) is that,
> while each inertial frame is
> it's own separate "world" with it's own clocks,
> light jumps [between] them
Stick with the ship departing normal to the ecliptic. Stick with
communication witnessed between the Earth and the Moon. It isn't
"superlumenal" if light is being used. Communication is observed to occur
at c*gamma (or less), as are all other phenomenon. Yes, things appear to
happen faster between the Earth and the Moon. That is where they are in
spacetime, compared to the ship.
Communications between the Earth and the ship concur with the ship's
expectation, given the *ship's* measurements of duration and distance.
Communication will always show propagation of c or less for the round trip.
Even triangulation will show the Earth being closer, from the ship's frame
(via "rotation").
David A. Smith
Tom Capizzi
How can you justify this assumption? In the first place, trips to the moon
and messages to Mars would not appear to take the same time in different
directions, and the only reason they appear to be qucker is the length
contraction along the direction of travel. Shorter paths cancel the notion
of superluminal.
DavidBowman
I just read the twin paradox faq, and it turns out that I didn't know
what the hell was going on -- an almost diurnal event, it feels like!
thanx guys,
=[ d
Paul Cardinale
is observer dependent.
Paul Cardinale
Ben Rudiak-Gould
> Yes, c is the same for everybody. However, the underlying "essence" of SR is
> that things that are simultaneous in one frame are not necessarily
> simultaneous in another. If you work through the twin-paradox problem, the
> solution is actually that for the Earth-bound twin, the clock on the
> spacecraft has run slow, but for the spacecraft-bound twin, it's the trip
> that has been shrunk. That fact can be easily shown from the Lorentz
> transformation.
Okay, I take issue with everything in that paragraph. In my opinion it's
exactly this kind of quasi-right, quasi-wrong description which leaves
people like DavidBowman confused.
In SR, everything happens in every frame. A reference frame is just
a way of assigning quadruples of values (x,y,z,t), also known as
"coordinates", to things that happen in the world. Every reference frame
assigns some quadruple of values to everything that happens. Different
reference frames assign different quadruples.
You can imagine physically constructing a reference frame by filling space
with clocks, each with an (x,y,z) label. When something happens, the time t
shown on the nearest clock, together with its label (x,y,z), gives you the
coordinates (x,y,z,t). Of course, you have to take care that the clocks you
introduced don't interfere with whatever you're actually measuring. And you
must use a nearby clock, because physics is local. It's not clear what it
would mean to take the reading of a faraway clock.
You can express the laws of physics in terms of the components x,y,z,t of
these quadruples. Depending on which reference frame you use, the laws may
look simpler or more complex (but of course they're the same laws in every
case).
There's a set of reference frames with the property that the laws, when
expressed in terms of the coordinates assigned by one of those frames, take
on a particularly simple form. They're called the "inertial reference
frames". In fact, the laws take on the /same/ form with respect to any of
these frames, so looking at the laws alone you can't tell which frame
they're meant to apply to, nor does it really matter. This reflects a
certain physical symmetry of the world, even though the reference frames
themselves are not physically real (unless you construct part of one).
There's a very close analogy between all of this and high-school analytic
geometry:
Spacetime <=> The Euclidean plane
Laws of physics <=> Geometric forms like circles
Reference frames <=> Coordinate systems
Coordinates <=> Coordinates
Laws of physics wrt RF <=> Equations like x^2 + y^2 = r^2
Inertial RFs <=> Cartesian coordinate systems
Lorentz "boost" <=> Rotation
Lorentz transformations <=> Cartesian coordinate transformations
In high school you first learn Euclidean geometry, which talks about forms
like triangles and circles. Then you learn about (x,y) coordinates, and how
to express the equation of a line or a circle in terms of coordinates. There
are all kinds of ways you could assign (x,y) coordinates to things on the
Euclidean plane, but there's a set of coordinate systems in which the
equations take on a particularly simple form -- in fact, the same form in
all of those coordinate systems. Those are the Cartesian coordinate systems
(or orthonormal coordinate systems in college-level linear algebra). Their
existence reflects a symmetry of Euclidean geometry
(rotational/translational invariance), even though the coordinate systems
themselves break that symmetry in a certain sense.
Different Cartesian coordinate systems (with the same origin) are related by
the following formulas, where (x,y) are the coordinates in one system,
(x',y') are the coordinate in the other, and theta is the angle between the
coordinate systems:
x' = x cos theta - y sin theta
y' = x sin theta + y cos theta
The coordinates of different inertial reference frames are related by these
formulas:
x' = x cosh alpha + t sinh alpha
t' = x sinh alpha + t cosh alpha
where (x,t) and (x',t') are the coordinates with respect to the two
reference frames, and alpha is the so-called "rapidity", which is a function
of the relative velocity V of the two frames. (We also have y'=y and z'=z,
just as we would if we introduced two new dimensions to the Euclidean case.)
That's the Lorentz transformation, written in a way that makes the
similarity to the Euclidean case more obvious. The similarity is not
coincidence.
Suppose you have two "vertical" lines in the Euclidean plane, with equations
x = 0 and x = 1 respectively. Now rotate the coordinate system by 45
degrees. The same two lines now have equations x = y and x = y+sqrt(2)
respectively. Note that, for any particular value of y, the x coordinates of
the two lines differ by sqrt(2), while in the original coordinate system
they only differed by 1. Is this a real change? Is it illusion? It's not
really either -- it's just an odd property of the coordinate representation.
Suppose you have two objects "at rest" with respect to an inertial reference
frame, with equations x = 0 and x = 1m respectively. Now do a Lorentz boost
by a relative speed of V = 0.707c. The same two objects now have equations x
= Vt and x = Vt + 0.707m. Note that, for any particular value of t, the x
coordinates of the two lines differ by 0.707 meter, where in the original
coordinate system they differed by 1 meter. This is the Lorentz-Fitzgerald
contraction. Is it real? Is it illusion? It's not really either -- it's just
an odd property of the coordinate representation. The gamma factor has the
same role in SR as the Pythagorean theorem has in analytic geometry.
The twin paradox is the triangle inequality.
It would be much better to write the laws of physics so that they didn't
talk about reference frames at all, just like the theorems of Euclidean
geometry don't talk about coordinate systems. No one has succeeded in doing
this, though there have been some interesting attempts (I wish I had
references handy). Physical laws can be written in a "manifestly
coordinate-invariant" way, but that just means they'll work /no matter which
coordinate system you choose/. It doesn't mean that they'll work /without a
coordinate system at all/, as Euclidean geometry does.
There's a huge difference between the notion of assigning (x,y,z,t) values
of events with respect to a reference frame, and the notion of what a
particular /person/ actually /sees/. Unfortunately physicists are in the
habit of saying "Joe sees..." when what they really mean is "Joe is moving
inertially, and with respect to an inertial reference frame in which Joe's
motion has the equation x=y=z=0, the coordinates of some other event
are...". Sometimes they're more careful and use "observes" in this sense and
"sees" only in the ordinary English sense. Even if you're aware of this
convention, there's a more serious problem: in general is doesn't even make
sense to talk about a reference frame corresponding to Joe. If Joe is not
moving inertially, there's no appropriate inertial reference frame. If Joe
changes speed, and you try to model this by changing reference frames, weird
non-physical things appear to happen (but don't really happen, of course),
like clocks running backwards. If Joe lives in curved spacetime, there are
no inertial reference frames in the first place. None of this affects what
Joe /sees/, because that's an actual physical action with a well-defined
meaning, regardless of Joe's motion. One example of this: If Alice and Bob
are walking alone the street in opposite directions, and look in the same
direction as they pass each other, what they /see/ at that moment will be
the same, ignoring aberration and Doppler shift. But what they "observe" at
that moment will be totally different. They will see the same time on the
clock in the town square, but in general they will observe different times.
Given the conciseness of "Joe observes" versus my alternate phrasing, I
suppose I understand why physicists use it. But it's very confusing to
students, and even to professional physicists sometimes. I'm not convinced
that Roger Penrose understands that his Andromeda-galaxy example from _The
Emperor's New Mind_ has no direct physical significance. I know that at
least one philosopher has argued that the relativity of simultaneity implies
that all of history must exist together, which is a classic example of
erroneous thinking along these lines.
Did that help at all?
> So the guy at 99.9%c sees 22.37 ticks per second, regardless of the
> directions of his travel due to time dilation. This is different from the
> Doppler shift in the carrier frequency, would be blue shifted if he is
> going toward Earth and red-shifted if traveling away.
The Doppler shifted frequency is what the guy will actually see. Depending
on the direction of his travel this may be anything from 44.7 ticks per
second to 44.7 seconds per tick. The figure of 22.37 ticks per second (which
I think should be 22.37 seconds per tick) is measured with respect to an
inertial reference frame comoving with the guy. It doesn't depend on the
direction of the guy's motion, because it also doesn't depend on his
position -- inertial reference frames aren't localized in space or time.
> [...] Doppler shift depends on the wave nature of light [...]
I think it's easier to understand the Doppler shift as an apparent speeding
up and slowing down of everything, not just wave oscillations. If a clock
appears blueshifted by a factor of 2, it will also appear to run at double
speed. These two facts are inseparable.
(The speed at which you hear it tick will depend on the Doppler formula for
sound, not that for light.)
> The signals still travel at speed c. Due to
> the velocity-addition formula, they are still limited by c.
Ah, the "velocity addition formula", a name seemingly calculated to confuse.
It's really a velocity transformation formula, of course. One of the
velocities in it is always the relative velocity of two reference frames.
The other is the velocity of some object (or another reference frame) with
respect to one of those reference frames.
If you're working in the coordinate system of just one reference frame, it's
never appropriate to use the velocity transformation formula. It's often
appropriate to truly add velocities, even if the result is a value larger
than c. If a train leaves Chicago at noon UTC travelling toward San
Francisco at speed v, and a light beam leaves San Francisco at noon UTC
travelling toward Chicago at speed c, at what time will they meet? The
answer is noon UTC plus d/(c+v), where d is the distance between S.F. and
Chicago. In this formula c+v effectively denotes the speed at which the
train and the light beam are approaching each other, with respect to the UTC
reference frame. SR teachers are probably afraid to show this example to
their students for fear of confusing them.
-- Ben
DavidBowman
Would you mind reminding me how one adds velocities so they don't
exceed c? Do you multiply them by gamma first (I think)?
BTW, do you multiply or divide by gamma? I don't remember if it
includes the "1/", or just the "sqrt(1-(v^2/c^2))".
> It would be much better to write the laws of [relativistic] physics
so that they didn't
talk about reference frames at all, just like the theorems of Euclidean
geometry don't talk about coordinate systems. No one has succeeded in
doing
this, though there have been some interesting attempts (I wish I had
references handy).
If you remember, please let me know!
Thanx,
=[ d
Bilge
>
>Would you mind reminding me how one adds velocities so they don't
>exceed c? Do you multiply them by gamma first (I think)?
just the hyperbolic tangent,
v_1/c = \beta_1 = tanh(A)
v_2/c = \beta_2 = tanh(B)
v_sum/c = \beta_3 = tanh(A+B) = [tanh(A) + tanh(B)]/[1 + tanh(A) tanh(B)]
(Assuming the velocities are collinear.) If the velocities are not
collinear, then break them into components.
DavidBowman
But what is the backslash operator?
=[ d
Paul B. Andersen
> This question was inspired by a single sentence in a post by Kenseto to
> prove his aether theory. He got the tongue-lashing he deserved... but
> the problem still haunts me.
>
> paradox that I can't resolve -- but hopefully you can, if you would be
> so very kind.
>
> ======
>
> earth fires an omnidirectional radio pulse. When that energy reaches
> the moon one second later, it's twin beacon on the moon detects it and
> fires another omnidirectional burst.
>
> One second after that, the radio pulse from the moon reaches earth and
> is detected by the earth beacon which fires another omnidirectional
> blast ...and so on.
>
> Each beacon is triggered by the other, and alternately fires a radio
> pulse every two seconds. So a guy on Mars hears a "click" on his radio
> reciever at one-second intervals.
>
> So far, so good.
>
> BUT:
> A guy in a spaceship moving .999c must also hear the same clicks at
> one-second intervals, since we all agree that the earth-moon distance
This is wrong for a number of reasons.
1. We do NOT all agree that the light-moon distance is 1 light second.
It will be very different in the spaceship-frame.
2. The speed of light is c in the spaceship-frame, but the Moon and
The Earth is moving at .999c, so the time for the light to go
from Earth-Moon or vice versa will be very different from 1 second
even if the distance were 1 light-second. (Depending on whether
the target recedes from or approaches the light.)
>
> The problem is that this gizmo can be used as a universal time standard
> -- literally. Everyone in the universe can listen to the master clock
> ticking away once per second, no matter how fast they're moving --
> including the two guys in the twin paradox.
We have two clocks ticking at the proper rate 0.5 Hz.
Why can these two clocks be considered "universal time standards"
any more than any other clock?
This is confused nonsense.
>
> The only way out I can see is if time dialation causes the guy in the
> spaceship to observe a light pulse travel from the earth to the moon in
> an arbitrarily short time, limited only by how fast his rocket can go.
>
> But if that's the case, you can get superluminal communication,
> because:
>
> 1) you can make radio travel from the earth to the moon in an
> arbitrarily short time, and
>
> 2) the space ship is a finite number of earth-moon distances away.
>
> =========
>
> "Well Hal, I'm damned if I can find anything wrong with it!"
> -- David Bowman to HAL9000 in the pod bay
>
> =[ d
>
Paul
DavidBowman
I KNOW that, Paul! I knew that when I posted it, because it forces a
contradiction with SR.
I wanted to know WHY it was wrong. Dirk kindly pointed me to the twin
paradox faq, and now I know.
Case closed.
=[ d